Get plane from 3D polygon and normal

Question

I have a polygon defined by n points and a polygon normal.

• Now I want to get the plane of the polygon defined by
  • a plane normal=(nx,ny,nz)
  • and a constant d (distance from the origin to the plane).
• The plane normal is equal to the polygon normal, but how can I calculate d?
• desired plane equation nx*x+ny*y+nz*z+d=0.0

Answer 1

Take any point p=(p_x, p_y, p_z) on the plane and plug it into the equation to obtain d.

So if your equation is n_x·x + n_y·y + n_z·z + d = 0 then you get d = − (n_x·p_x + n_y·p_y + n_z·p_z).

Another common formulation is using d as the right hand side of the equation, in which case you get the reverse sign. I.e. for the equation n_x·x + n_y·y + n_z·z = d you get d = n_x·p_x + n_y·p_y + n_z·p_z.